This document discusses risk and expected rate of return in investments. It defines risk as the level of uncertainty associated with an expected outcome like rate of return. Investors prefer lower risk for a given expected return. There is a tradeoff between risk and return, with more aggressive investors willing to take on higher risk for higher return. Infrastructure projects generally have large investments, long timelines, low returns but high risk. Risk in investments can be measured by variance and is a key factor in financial decisions.

2.  Expected Rate of Return : Rate of Return with
respect to future cash-flows
 How sure are your prediction ?
 It could take a wide range of values.
 Range, Band, Spectrum
 Rate of Return [k] needs to be qualified by its level of
certainty
 Can there be a measure for this certainty?

3.  The level of uncertainty with respected to an
expected outcome [ example: Rate of Return] is
called ‘Risk’ of that outcome.
 The description of an expected [future]
outcome has two elements:
 Its value
 Its risk
 What is the physical significance of ‘Risk’?

4.  A project is under planning. Ask 100 experts on
the expected outcome of the project.
 The average of the 100 values will be the expected
value
 The variance of the distribution of values will
represent its uncertainty or risk.
 Higher the uncertainty, higher is the risk
 What relevance is the risk for the investor?

5.  For a given Expected rate of return an Investor
would prefer the option that offers lower risk.
 There will be a trade-off between risk and
return.
 Each investor would have a limit of the risk he/she
is inclined to take
 Some investors are aggressive; they can take higher risk
and look for higher return. [Gambler]
 Some investors would prefer lower risk even if the
return is lower. [Safe Bet]
 In every investment opportunity it is desirable to
profile the risk along with the return

6.  Project categories based on risk profile
 A project [or an investment opportunity] with
moderate risk tends to have moderate return
 A project with significantly high return would
invariably have high risk
 An investment opportunity with normal risk-
return profile is called a project
 An investment opportunity with high risk-
return profile is called a ‘Venture’

7.  What is the risk profile of an infrastructure
project?
 Infra-projects are generally characterised by
 Large investment
 Long life of project
 Long implementation period
 Low return
 High risk
 Examples of Infra-projects

8.  Elements of Risk
 Business risk
 Technology risk
 Market risk
 Financial risk
 Industry risk
 Economy/market/Country risk

9.  How do you measure risk?
 Wherever possible variance [ σ2] is the measure of
risk
 Rating agencies have a system of assessing risk
profiles and indicating them on certain relative basis
[S&P, Moodys, CRISIL, ICRA etc.]
 Where do you use such measures?
 Wide usage of ratings in the financial market
 Investment decisions are guided by risks